Up tack (original) (raw)
垂直記号（すいちょくきごう）は「⊥」の形をした幾何学で用いられる記号である。
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| dbo:abstract | En logique et en informatique, le taquet vers le haut, base, ou dessous, aussi appelé antitruc ou faux, noté ⊥, désigne la contradiction, c'est-à-dire la formule constante représentant le faux. Par exemple, la formule (P ∧ ¬P) ⇒ ⊥ signifie que la conjonction d'une proposition P et de son contraire non-P entraîne une contradiction. La formule se lit « P et non-P entraîne le faux ». Ce symbole peut aussi désigner le type vide en théorie des types, ou encore le plus petit élément d'un ensemble ordonné. L'usage des dénominations anglaises UP TACK, base, bottom (bot en abrégé) est également courant dans les pays francophones. Le glyphe de ⊥ est identique à celui de la relation mathématiques de perpendicularité en géométrie ou plus généralement d'orthogonalité en algèbre linéaire. (fr) The up tack or falsum (⊥, \bot in LaTeX, U+22A5 in Unicode) is a constant symbol used to represent: * The truth value 'false', or a logical constant denoting a proposition in logic that is always false (often called "falsum" or "absurdum"). * The bottom element in wheel theory and lattice theory, which also represents absurdum when used for logical semantics * The bottom type in type theory, which is the bottom element in the subtype relation. This may coincide with the empty type, which represents absurdum under the Curry–Howard correspondence as well as * Mixed radix decoding in the APL programming language The glyph of the up tack appears as an upside-down tee symbol, and as such is sometimes called eet (the word "tee" in reverse). Tee plays a complementary or dual role in many of these theories. The similar-looking perpendicular symbol (⟂, \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent: * Perpendicularity of lines in geometry * Orthogonality in linear algebra * Independence of random variables in probability theory * Coprimality in number theory The double tack up symbol (⫫, U+2AEB in Unicode) is a constant symbol used to represent: * Conditional independence of random variables in probability theory (en) 垂直記号（すいちょくきごう）は「⊥」の形をした幾何学で用いられる記号である。 (ja) |
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| rdfs:comment | 垂直記号（すいちょくきごう）は「⊥」の形をした幾何学で用いられる記号である。 (ja) En logique et en informatique, le taquet vers le haut, base, ou dessous, aussi appelé antitruc ou faux, noté ⊥, désigne la contradiction, c'est-à-dire la formule constante représentant le faux. Par exemple, la formule (P ∧ ¬P) ⇒ ⊥ signifie que la conjonction d'une proposition P et de son contraire non-P entraîne une contradiction. La formule se lit « P et non-P entraîne le faux ». Ce symbole peut aussi désigner le type vide en théorie des types, ou encore le plus petit élément d'un ensemble ordonné. (fr) The up tack or falsum (⊥, \bot in LaTeX, U+22A5 in Unicode) is a constant symbol used to represent: * The truth value 'false', or a logical constant denoting a proposition in logic that is always false (often called "falsum" or "absurdum"). * The bottom element in wheel theory and lattice theory, which also represents absurdum when used for logical semantics * The bottom type in type theory, which is the bottom element in the subtype relation. This may coincide with the empty type, which represents absurdum under the Curry–Howard correspondence as well as (en) |
| rdfs:label | ⊥ (fr) 垂直記号 (ja) Up tack (en) |
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